On the Equivalence of the SMO and MDM Algorithms for SVM Training
Abstract
SVM training is usually discussed under two different algorithmic points of view. The first one is provided by decomposition methods such as SMO and SVMLight while the second one encompasses geometric methods that try to solve a Nearest Point Problem (NPP), the Gilbert–Schlesinger–Kozinec (GSK) and Mitchell–Demyanov–Malozemov (MDM) algorithms being the most representative ones. In this work we will show that, indeed, both approaches are essentially coincident. More precisely, we will show that a slight modification of SMO in which at each iteration both updating multipliers correspond to patterns in the same class solves NPP and, moreover, that this modification coincides with an extended MDM algorithm. Besides this, we also propose a new way to apply the MDM algorithm for NPP problems over reduced convex hulls.
Cite
Text
Lázaro et al. "On the Equivalence of the SMO and MDM Algorithms for SVM Training." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2008. doi:10.1007/978-3-540-87479-9_37Markdown
[Lázaro et al. "On the Equivalence of the SMO and MDM Algorithms for SVM Training." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2008.](https://mlanthology.org/ecmlpkdd/2008/lazaro2008ecmlpkdd-equivalence/) doi:10.1007/978-3-540-87479-9_37BibTeX
@inproceedings{lazaro2008ecmlpkdd-equivalence,
title = {{On the Equivalence of the SMO and MDM Algorithms for SVM Training}},
author = {Lázaro, Jorge López and Jiménez, Álvaro Barbero and Dorronsoro, José R.},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
year = {2008},
pages = {288-300},
doi = {10.1007/978-3-540-87479-9_37},
url = {https://mlanthology.org/ecmlpkdd/2008/lazaro2008ecmlpkdd-equivalence/}
}